Elliot Dear Esq | Production Function

1. Elliot Dear esq

2. Definition and example of Production Function. Types of Production Function. Law Of Production Function. Law of Variable Proportions. Production Function with one Variable Input.  Production Function with two Variable Inputs. Assumption. Summary. FURTHER READINGS

3. Production refers to the transformation of inputs or resources into outputs of goods and services. In other words, production refers to all of the activities involved in the production of goods and services, from borrowing to set up or expand production facilities, to hiring workers, purchasing row materials, running quality control, cost accounting, and so on, rather than referring merely to the physical transformation of inputs into outputs of goods and services.

4. A computer company hires workers to use machinery, parts, and factories to produce personal computers. The output of a firm can either be a final commodity or an intermediate product such as computer and semiconductor respectively. The output can also be a service rather than a good such as education, medicine, banking etc. raw materials in

5. Mathematical representation of the relationship: Q = f (K, L, La) Output (Q) is dependent upon the amount of capital (K), Land(L) and Labour (La) used

6. There are two distinct types of production function that show possible range of substitution inputs in the production process. 1. Fixed proportion Production function 2. Variable proportions production function

7. Short term : Time when one input (say, capital) remains constant and an addition to output can be obtained only by using more labour. Long run: Both inputs become variable. Production process is subject to various phases- Laws of production state the relationship between output and input.

8. Short run : Relationship between input and output are studied by varying one input , others being held constant. Law of Variable Proportions brings out relationship between varying proportions of factor inputs and output Long run: Production function is subject to different phases described under the Law of Returns to Scale – Studied assuming that all factor inputs are variable.

9. Law of Variable Proportions (Short run Law of Production) Assumptions: One factor (say, L) is variable and the other factor (say, K) is constant Labour is homogeneous Technology remains constant Input prices are given

10. No of Workers L Total Product (TPl) Marginal Average Stages of Returns Product (MPl) 24 48 66 78 84 84 78 66 48 24 -6 -42 Product (APl) 24 36 46 54 60 64 66 66 64 60 54 46 1 2 3 4 5 6 7 8 9 10 11 12 24 72 138 216 300 384 462 528 576 600 594 552 I) Increasing Returns II) Diminishing Returns III) Negative Returns 10

11. Panel A TP rises at an increasing rate till the employment of the 5th worker. TPl T o t a l p r o d u c t Beyond the 6thworker until 10th worker TP increases but rate of increase begins to fall Total Product TP turns negative from 11th worker onwards. u d o r P l a t o T This shows Law of Diminishing Marginal returns Labour 11

12. Panel B Panel B represents Marginal and average productivity curves of labour AP/MP APL M P L MPL labour 12

13. Increasing Returns- Stage I: TPlincreases at an increasing rate. Fixed factor (K) is abundant and variable factor is inadequate. Hence K gets utilized better with every additional unit of labour Stage II- TPlcontinues to increase but at a diminishing rate. stage III- TPlbegins to decline –Capital becomes scarce as compared to variable factor. Hence over utilization of capital and setting in of diminishing returns Causes of 3 stages: Indivisibility and inelasticity of fixed factor and imperfect substitutability between K and L 13

14. Significance of Law of Diminishing Marginal Returns: - Empirical law, frequently observed in various production activities - Particularly in agriculture where natural factors (say land), which play an important role, are limited. - Helps manager in identifying rational and irrational stages of operation 14

15. - It provides answers to questions such as: a) How much to produce? b) What number of workers (and other variable factors) to employ in order to maximize output In our example, firm should employ a minimum of 7 workers and maximum of 10 workers (where TP is still rising) 15

16. - Stage III has very high L-K ratio- as a result, additional workers not only prove unproductive but also cause a decline in TPl. - In Stage I capital is presumably under- utilised. - So a firm operating in Stage I has to increase L and that in Stage III has to decrease labour. 16

17. There are two Variable Proportions Production Function_ 1- Production Function With One Variable Input. 2- Production With Two Variable Inputs

18. ⚫ When discussing production in the short run, three definitions are important: ➢ Total product ➢ Marginal product ➢ Average product 18

19. Total Product TP = Q = f(L) TP L Marginal Product MPL= APL=TP Average Product L Production or Output Elasticity MPL APL EL= 19

20. Total Product ⚫ Total product (TP) is another name for output in the short run. TP = Q = f (L) 20

21. ⚫ The marginal product (MP) of a variable input is the change in output (or TP) resulting from a one unit change in the input. ⚫ MP tells us how output changes as we change the level of the input by one unit. ⚫ Consider the two input production function Q=f (L,K) in which input L is variable and input K is fixed at some level. ⚫ The marginal product of input L is defined as holding input K constant. TP L MPL= 21

22. ⚫ The average product (AP) of an input is the total product divided by the level of the input. ⚫ AP tells us, on average, how many units of output are produced per unit of input used. ⚫ The average product of input L is defined as holding input K constant. APL=TP L 22

23. Total, Marginal, and Average Product of Labor, and Output Elasticity MPL - 3 5 4 2 0 -2 APL - 3 4 4 3.5 2.8 2 EL - 1 1.25 1 0.57 0 -1 L 0 1 2 3 4 5 6 Q 0 3 8 12 14 14 12 23

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25. -In the long run, all inputs are variable. Isoquants show combinations of two inputs that can produce the same level of output. -In other words, Production isoquant shows the various combination of two inputs that the firm can use to produce a specific level of output. -Firms will only use combinations of two inputs that are in the economic region of production, which is defined by the portion of each isoquant that is negatively sloped. -A higher isoquant refers to a larger output, while a lower isoquant refers to a smaller output. 25

26. Isoquants K 6 5 4 3 2 1 Q 10 24 31 36 40 39 12 28 36 40 42 40 12 28 36 40 40 36 10 23 33 36 36 33 7 18 28 30 30 28 3 8 12 14 14 12 1 2 3 4 5 6 L 26

27.  THE PRODUCTION FUNCTIONS ARE BASED ON CERTAIN ASSUMPTIONS.  1 Perfect divisibility of both inputs and outputs  2 Limited substitution of one factor for another  3 Constant technology  4 Inelastic supply of fixed factors in the short run

28. A production function specifies the maximum output that can be produced with a given set of inputs. In order to achieve maximum profits the production manager has to use optimum input-output combination for a given cost. In this unit, we have shown how a production manager minimizes the cost for a given output in order to maximize the profit. Also, we have shown how to maximize the output at a given level of cost.

29. Adhikary, M (1987), Managerial Economics (Chapter V), Khosla,Publishing House, Delhi. Google.